Calculations for a general maximum principle: 1993 notes on the normalized parabolic $p$-Laplacian
Year: 2026
Type: preprint
Abstract: This note makes available, in facsimile form, a set of handwritten notes from September 1993 devoted to Bochner-type maximum principle computations for a general class of quasilinear parabolic equations which contains, as a special instance, the normalized parabolic $p$-Laplacian \[ u_t = Δu + (p-2)\,|\nabla u|^{-2}\,\nabla^2u(\nabla u,\nabla u). \] The notes were acknowledged in the introduction of the paper of Jin and Silvestre \cite{JS}, and the scheme they propose has recently been implemented in \cite{BGM} to obtain the sharp Li-Yau inequality for this equation. They are reproduced here verbatim, with no alterations, preceded by a brief introduction explaining their content and the subsequent history of the equation.
Source: arXiv (Cornell University)
Author: Garofalo, Nicola
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213250932